Folding Fractal Art from 49,000 Business Cards

The Mosely Snowflake Sponge in all its fractal glory. Photo: courtesy Hugh McHarg.

The art of folding paper is usually a solitary, meditative endeavor. But when your origami project involves 49,000 business cards and a healthy dose of non-Euclidean geometry, you probably want to enlist some help.

Beginning today, The USC Libraries are displaying an origami model of the Mosely Snowflake Sponge, a newly discovered three-dimensional fractal object designed by MIT-trained engineer Dr. Jeannine Mosely. The six-foot-tall structure consists of nothing but tens of thousands of business cards folded into paper cubes paneled with the school’s red and gold colors. The finished project is a group effort; Mosely enlisted the help of Margaret Wertheim, director of the Institute for Figuring and USC’s first Discovery Fellow, as well as several hundred volunteer folders, to help realize her vision.

The Snowflake Sponge resembles a hollow cube with each corner removed (termed “Level 1”). The Level 1 blocks are used as the components for a larger version of themselves — Level 2 — and so forth. Mosely’s installation at USC is a Level 3 fractal.

But while the math behind the Snowflake Sponge’s repetitive structure is fairly straightforward, figuring out how to assemble its final form was anything but. “Not only are we building a mathematical object that’s never been made before, [but] it’s a huge challenge of engineering,” Wertheim told me. “How can you actually put this structure together?” After trying out a few mathematically elegant strategies, the team settled on a method based on x- and y-modules, which are “basically Level 1s with a few cubes missing.” That extra empty space made it easier for Wertheim and her assistants to link the modules into spines that form the structural basis for the Snowflake Sponge.

Their module method created the added benefit of utilizing a kind of origami production line. Hundreds of students and other volunteers contributed to the project over the past seven months, building cubes, assembling modules, or even just creasing business cards. “In that sense it’s a really substantial community art project,” says Wertheim, who was able to focus on the more delicate work of assembling the spines and constructing the Level 3 thanks to the thousands of hours of volunteer labor.

This isn’t Mosely and Wertheim’s first foray into crowdsourced origami. In 2006, they worked together to build a business card model of the Menger Sponge, the first three-dimensional fractal ever discovered and a close mathematical relative of the Snowflake Sponge. Volunteers from all over the country built the model out of 66,000 of Mosely’s own out-of-date business cards; the team displayed the finished product at Machine Project in Los Angeles.

While Mosely also does technically sophisticated curved-crease origami, she is drawn to the repetitive elegance of fractals and how they lend themselves to participation from even the most novice folder. If her curved-creased pieces resemble delicate sculptures, teaching hundreds of people to fold cubes and assemble modules is like conducting an orchestra. Mosely compared the Snowflake Sponge project to a performance that can be repeated on many scales — much like the infinitely self-similar fractal it has created.

The Mosely Snowflake Sponge will be on display in the rotunda of USC’s Doheny Memorial Library through the end of the year, along with an exhibit about the mathematics of fractals and the engineering challenges the team faced.

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